There are a number of situations in which it is desirable to be able to estimate accurately position in a hydrocarbon well borehole. For example:                when making a wireline log or analysing a slickline log, the position of the logging tool is needed when each measurement is made;        when intervening in a well with coiled tubing, the position of the tool at the end of the tubing is required;        when drilling, the location of the bottom hole assembly (BHA) and bit is needed; and        when inserting an autonomous device (e.g. of the type disclosed in U.S. Pat. No. 6,405,798) into a well, the device should be able to determine its own position for navigation.        
For each of these situations, application-specific dead-reckoning approaches to estimate position may be adopted. For example, one approach is to measure the length of wireline, drill pipe or coiled tubing reeled out. Alternatively, on a wheeled downhole device an odometer can be used to measure distance travelled.
A dead-reckoning technique widely used in other technical fields is inertial navigation. In general, to estimate an arbitrary change in position, three accelerometers are needed to measure acceleration in three directions, the measurements being integrated twice. U.S. Pat. Nos. 4,945,775 and 4,812,977 disclose inertial navigation systems for use in wellbores which have three accelerometers. However, at least for the purpose of depth correction in an essentially one-dimensional system, such as a wellbore, three accelerometers are sometimes not necessary. For example, U.S. Pat. No. 5,522,260 discloses a procedure for performing depth correction on a logging tool having two spaced logging sensors in which the tool is provided with one accelerometer. In the procedure, the tool velocity determined by correlating the sensor logs is combined with the tool velocity determined by the accelerometer to produce a depth correction for the tool.
Physical models may also be employed to improve the accuracy of the dead-reckoning calculation. For example, U.S. Pat. No. 4,843,875 describes a procedure for measuring drill bit rate of penetration which assumes that the behaviour of the drill string can be modelled by an equation which relates instantaneous drill bit velocity to the instantaneous velocity of the drill string at the surface, the apparent compliance of the drill string, and the first derivative with respect to time of the weight suspended from the hook.
However, all of these approaches are subject to various types of error: wheels with odometers may slip, coiled tubing has a tendency to coil in the borehole, double integration magnifies errors, models of elasticity and friction may not be accurate. Because of this, when using dead-reckoning the magnitude of the error tends to increase with distance travelled.
Consequently, other approaches to position determination within boreholes are sometimes used. One approach is based on landmark recognition. Downhole devices may be fitted, for example, with casing collar locators (CCL) which can sense when the tool is adjacent a casing joint. However, a CCL may occasionally fail to detect an adjacent casing collar, or may spuriously detect a non-existent collar, due to noise. Because the sensors are usually not able to distinguish between different casing collars, this results in uncertainty in position. Moreover, if a logging tool fitted with a CCL encounters a fork in a bore, it may not be clear merely from the CCL reading, which branch of the bore has been followed by a logging tool. Furthermore, for absolute (as opposed to relative) position determination, the positions of the casing joints must be known beforehand.
Another approach is to provide the downhole device with a sensor which is able to measure some characteristic of the wellbore environment, for example a gamma-ray sensor to measure the amount of gamma-rays emanating from the surrounding rock formation. If the gamma-ray profile of the well is known, the sensor readings can be correlated with the profile and position determined in this way. This form of position determination is called map-matching. However, map-matching can affected by sensor noise, as well as suffering from drawbacks similar to those associated with landmark recognition.
Although unrelated to the technical field of the present invention, a navigation technique has been developed by Thrun and co-workers (see Thrun, Fox, Burgard and Dellaert, Robust Monte Carlo Localization for Mobile Robots, Artificial Intelligence Journal, 2000). The technique was developed for use by a wheeled mobile robot operating in an environment of rooms and corridors. It uses information from wheel odometers, laser and sonar range-finders, and a TV camera that looks at the ceiling.
The Monte Carlo Localization (MCL) approach adopted by Thrun and co-workers is a Bayesian method that estimates a probability distribution function (PDF) for the location (and orientation) of the robot. Whenever the robot moves, the PDF can be updated using a predictive stochastic model of the robot motion and observational data from the sensors.